That should not be the definition of purpose - if we are trying to be scientific. Martian scientists should come to the same conclusions.
Do you mean that a Martian scientist would not conclude that when a human being uses that word, they are referring to a particular part of their brain that is being stimulated?
What I'm saying is that the notion of "purpose" is an interpretation we project onto the world: it is a characteristic of the map, not of the territory.
To put it another way, there are no purposeful things, only things that "look purposeful to humans".
Another mind with different purpose-detecting circuitry could just as easily come to different conclusions -- which means that the Martians will be led astray if they have different purpose-recognition circuits, following which we will have all sorts of arguments on the boundary conditions where human and Martian intuitions disagree on whether something should be called "purposeful".
tl;dr: if it's part of the map, the description needs to include whose map it is.
"Purpose" - in this kind of context - could mean "goal directed" - or it could mean pursuing a goal with a mind that predicts the future.
Now you have to define "mind" as well. It doesn't seem to me that that's actually reducing anything here. ;-)
Most scientific definitions should try to be short and sweet. Definitions that include a description of the human mind are ones to eliminate.
Here, the idea that purpose is a psychological phenomenon is exactly what was intended to be avoided - the idea is to give a nuts-and-bolts description of purposefulness.
Re: defining "mind" - not a big deal. I just mean a nervous system - so a dedicated signal processing system with I/O, memory and processsing capabilities.
Sweet, there's another Bloggingheads episode with Eliezer.
Bloggingheads: Robert Wright and Eliezer Yudkowsky: Science Saturday: Purposes and Futures